6.4 Chemical Dosing, Feed Rate & Quantity Calculations

6.4 Chemical Dosing, Feed Rate & Quantity Calculations

Exam Focus: Collection operators must master the universal pounds formula (lbs/day = MGD × mg/L × 8.34), adjust calculations for liquid chemical specific gravity (SG) and percent concentration, and compute metering pump calibration rates in gallons per day (gpd) and milliliters per minute (mL/min).

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The Universal Pounds Formula

The most widely used mathematical relationship in wastewater treatment and collection system chemical dosing is the pounds formula. This formula calculates the total weight of pure chemical required per day based on wastewater flow volume and target chemical dosage.

$\mathbf{\text{lbs/day} = \text{Flow (MGD)} \times \text{Dosage (mg/L)} \times 8.34\text{ lbs/gal}}$

                      THE POUNDS FORMULA TRIANGLE

                             [  lbs/day  ]
                            +-------------+
                            | Flow | Dose |
                            | (MGD)|(mg/L)| × 8.34
                            +-------------+

    To solve for lbs/day:    lbs/day = MGD × mg/L × 8.34
    To solve for Dosage:     Dosage (mg/L) = (lbs/day) / (MGD × 8.34)
    To solve for Flow:       Flow (MGD) = (lbs/day) / (Dosage × 8.34)

Why the 8.34 lbs/gal Constant Works

• 1 gallon of water = 8.34 pounds.
• 1 milligram per liter (mg/L) = 1 part per million (ppm) by weight in water.
• Therefore, 1 mg/L in 1.0 Million Gallons (MG) of water equals: $1.0\text{ MG} \times 8.34\text{ lbs/gal} \times \frac{1\text{ lb}}{1{,}000{,}000\text{ lbs}} = \mathbf{8.34\text{ pounds}}$

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Liquid Chemical Dosing Adjustments

Chemicals utilized in collection systems (e.g., ferric chloride, calcium nitrate, sodium hypochlorite, sodium hydroxide) are supplied as liquid solutions rather than 100 percent pure dry powders. Liquid calculations require two adjustments:

1. Specific Gravity (SG): The ratio of the solution's density compared to pure water (1.00). $\text{Weight of 1 Gallon of Chemical Solution} = 8.34\text{ lbs/gal} \times \text{SG}$
2. Percent Active Strength (Percent Concentration): The fraction of total solution weight that is active chemical ingredient. $\mathbf{\text{Pounds of Active Chemical per Gallon} = 8.34 \times \text{SG} \times \left(\frac{\text{Percent Active Strength}}{100}\right)}$

                 LIQUID CHEMICAL BULK WEIGHT DERIVATION

    Pure Water (SG = 1.0)               Bulk Chemical Solution (e.g., FeCl3)
    +--------------------+              +--------------------+
    | Density = 8.34     |              | Specific Gravity = 1.42            |
    | lbs per gallon     |              | Total Weight = 1.42 × 8.34         |
    |                    |              |              = 11.84 lbs/gallon    |
    |                    |              | Active Strength = 40% FeCl3        |
    |                    |              | Active lbs/gal = 11.84 × 0.40      |
    |                    |              |                = 4.74 lbs/gal      |
    +--------------------+              +--------------------+

Liquid Feed Rate Formulas

• Daily Volume Feed Rate (gal/day): $\mathbf{\text{Feed Rate (gal/day)} = \frac{\text{Required lbs/day of Active Chemical}}{\text{Pounds of Active Chemical per Gallon}} = \frac{\text{Flow (MGD)} \times \text{Dosage (mg/L)}}{\text{SG} \times \left(\frac{\text{Percent Active Strength}}{100}\right)}}$

• Feed Rate in Gallons per Minute (gpm): $\text{Feed Rate (gpm)} = \frac{\text{Feed Rate (gal/day)}}{1{,}440\text{ min/day}}$

• Feed Rate in Milliliters per Minute (mL/min): $\mathbf{\text{Feed Rate (mL/min)} = \frac{\text{Feed Rate (gal/day)} \times 3{,}785.4\text{ mL/gal}}{1{,}440\text{ min/day}} = \text{Feed Rate (gal/day)} \times 2.6288}$

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Collection System Chemical Application Summary

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Metering Pump Calibration Tubes

To verify that a positive displacement chemical metering pump is delivering the exact specified dosage, operators perform a drawdown tube calibration test.

                   CHEMICAL CALIBRATION CYLINDER

                   [  Graduated Cylinder  ]
                   |       1000 mL        |
                   |        800 mL        |   1. Isolate bulk tank
                   |        600 mL        |   2. Run pump for 60 seconds
                   |        400 mL        |   3. Measure mL consumed
                   |        200 mL        |   4. Compare: Observed mL/min
                   +----------------------+      vs. Calculated mL/min
                             |
                             v  (To Metering Pump Suction)

$\text{Target Flow (mL/min)} = \text{Feed Rate (gal/day)} \times 2.6288$

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Step-by-Step Worked Dosing Problems

Problem 1: Basic Pounds Formula (Oxidizer Dosing)

Question: A wastewater utility doses an interceptor main flowing at 2.40 MGD with an odor control chemical at a target dosage of 15.0 mg/L. How many pounds of chemical are consumed per day?

• Step 1: Apply pounds formula: $\text{lbs/day} = \text{Flow (MGD)} \times \text{Dosage (mg/L)} \times 8.34\text{ lbs/gal}$ $\text{lbs/day} = 2.40\text{ MGD} \times 15.0\text{ mg/L} \times 8.34 = \mathbf{300.24\text{ lbs/day}} \approx \mathbf{300.2\text{ lbs/day}}$

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Problem 2: Liquid Chemical Feed Rate (Ferric Chloride)

Question: A collection system must feed 450.0 lbs/day of pure ferric chloride ($\text{FeCl}_3$) to precipitate sulfides in a trunk sewer. The bulk ferric chloride liquid solution has a Specific Gravity of 1.40 and contains 38.0 percent active $\text{FeCl}_3$ by weight. Calculate the liquid chemical feed rate in gallons per day (gal/day).

• Step 1: Calculate total weight of one gallon of bulk solution: $\text{Total Weight per Gallon} = 8.34\text{ lbs/gal} \times 1.40\text{ SG} = 11.676\text{ lbs/gal}$
• Step 2: Calculate pounds of active chemical per gallon: $\text{Active lbs/gal} = 11.676\text{ lbs/gal} \times 0.380 = 4.4369\text{ lbs active/gal}$
• Step 3: Calculate required gallons per day: $\text{Feed Rate (gal/day)} = \frac{450.0\text{ lbs/day}}{4.4369\text{ lbs active/gal}} = \mathbf{101.4\text{ gal/day}}$

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Problem 3: Calibration Tube Flow Rate in mL/min

Question: A metering pump feeding calcium nitrate solution is set to deliver 72.0 gallons per day. During a 1.0-minute calibration cylinder test, how many milliliters (mL) of chemical should be drawn down by the pump?

• Step 1: Convert daily gallons to daily milliliters: $\text{mL/day} = 72.0\text{ gal/day} \times 3{,}785.4\text{ mL/gal} = 272{,}548.8\text{ mL/day}$
• Step 2: Convert to milliliters per minute: $\text{mL/min} = \frac{272{,}548.8\text{ mL/day}}{1{,}440\text{ min/day}} = \mathbf{189.3\text{ mL/min}}$
• Direct Shortcut (72.0 gal/day × 2.6288 = 189.3 mL/min): Confirmed.